We investigate the state space reconstruction from multiple time series derived from continuous and discrete systems and propose a method for building embedding vectors progressively using information measure criteria regarding past, current, and future states. The embedding scheme can be adapted for different purposes, such as mixed modeling, cross-prediction and Granger causality. In particular, we apply this method in order to detect and evaluate information transfer in coupled systems. As a practical application, we investigate in records of scalp epileptic EEG the information flow across brain areas.

The turbulent diffusivity tensor is determined for linear shear-flow turbulence using numerical simulations. For moderately strong shear, the diagonal components are found to increase quadratically with Peclet and Reynolds numbers below about 10 and then become constant. The diffusivity tensor is found to have components proportional to the symmetric and antisymmetric parts of the velocity gradient matrix, as well as products of these. All components decrease with the wave number of the mean field in a Lorentzian fashion. The components of the diffusivity tensor are found not to depend significantly on the presence of helicity in the turbulence. The signs of the leading terms in the expression for the diffusion tensor are found to be in good agreement with estimates based on a simple closure assumption.

Motivated by recent experiments, we extend the Joanny-deGennes calculation of the elasticity of a contact line to an arbitrary contact angle and an arbitrary plate inclination in presence of gravity. This requires a diagonalization of the elastic modes around the nonlinear equilibrium profile, which is carried out exactly. We then make detailed predictions for the avalanche-size distribution at quasistatic depinning: we study how the universal (i.e., short-scale independent) rescaled size distribution and the ratio of moments of local to global avalanches depend on the precise form of the elastic kernel.

We investigate the kinetics of general two species annihilation $nA+mB\to 0$ of driven hard-core (HC) particles with $N=n+m$ in one dimension. With uniform drift velocity, all particles are driven to the right. HC exclusion forbids the interchange of any particles and restricts the number of particles on a site to 0 or 1. The reaction is classified into two classes, the symmetric and the asymmetric reaction. The symmetric reaction means both $nA+mB\to 0$ and $mA+nB\to 0$, while the asymmetric reaction means only $nA+mB\to 0$ for a given $\left(n,m\right)$ pair. As $N$ increases, the trains of particles causing the reaction rarely form. Hence, for sufficiently large $N$, particles are evenly distributed before the reaction, so one expects a crossover $N_c$ above which the kinetics follows the classical mean-field rate equation. We show the existence of $N_c$ and that the kinetics for $N<N_c$ is the same as that of $A+B\to 0$ of driven HC particles as in the reactions with the isotropic diffusion. However, compared to the isotropic cases, $N_c$ and the kinetics for $N\ge N_c$ are shown to be completely changed by the interplay of the drift and HC exclusion, and strongly depend on the reaction symmetry. We also show that densities decay as $t^{-1/N}$ which cannot be explained by the classical mean-field rate equation. Instead the kinetics is explained analytically by a variant theory.

In this paper we consider the effect of different time parametrizations on the stationary velocity distribution function for a relativistic gas. We clarify the distinction between two such distributions, namely, the Jüttner and the Modified Jüttner distributions. Using a recently proposed model of a relativistic gas, we show that the obtained results for the proper-time averaging does not lead to the Modified Jüttner distribution (as recently conjectured), but introduces a Lorentz factor $\gamma \left(\mathbf{v}\right)$ (i.e., energy) to the well-known Jüttner function which results from observer-time averaging. These two modifications (i.e., Modified Jüttner function or Jüttner divided by energy) are identical in the rest frame; however, their distinction comes to light when one considers a moving frame. We obtain results for rest frame as well as moving frame in order to support our claim. We finally conclude that reparametrizing time simply rescales stationary (Jüttner) distribution function according to a well-defined frame-independent relation.

The critical behavior of the pitch divergence of cholesteric liquid crystals in the vicinity to smectic-$A^{\ast }$ $\left(\text{Sm}{A}^{\ast }\right)$ and smectic-$C^{\ast }$ $\left(\text{Sm}{C}^{\ast }\right)$ phases is studied experimentally and compared with conflicting theoretical interpretations. Members of two homologous series were studied with varying polymorphism from ${\text{N}}^{\ast }\text{-Sm}{C}^{\ast }$ to ${\text{N}}^{\ast }\text{-Sm}{A}^{\ast }$. A modified functionality of the temperature dependence of the pitch is introduced to determine the critical exponent, and it is shown that the latter is independent of sample geometry. In contrast to several earlier investigations aiming to determine the critical exponent, which were inconclusive, the results of our critical exponents for the pitch divergence provide evidence for the model by Chen and Lubensky which predicts a critical exponent of $\nu =1/2$ for the ${\text{N}}^{\ast }\text{-Sm}{A}^{\ast }$ and $\nu =1$ for the ${\text{N}}^{\ast }\text{-Sm}{C}^{\ast }$ transition. This specifically implies that fluctuations cannot be neglected in the consideration of the nature of the phase transition.

A recent paper by Zinin et al. [Phys. Rev. E 79, 021910 (2009)] regarding the dynamics of biological cells in an acoustic field draws conclusions that we find open to debate. The present paper examines these conclusions and addresses some findings.

We investigate propagation and control of weak-light spatial solitons in a resonant three-level atomic system with a periodic modulated control field. It is shown that the periodic modulation acts like periodic potential which resists the propagation of the soliton in transverse direction. The soliton could be trapped by the periodic potential in the input channel. When the modulation is canceled, the soliton propagates in its initial incident direction. The periodic modulation of control field could be used to control the propagation of the weak-light probe soliton. Due to the good localization efficiency of the periodic potential, an excellent switching is realized for the probe soliton. These properties may have potential applications in all-optical switching, optical information processing and other fields.

We propose a degree-based coarse-graining approach that not just accelerates the evaluation of dynamics on complex networks, but also satisfies the consistency conditions for both equilibrium statistical distributions and nonequilibrium dynamical flows. For the Ising model and susceptible-infected-susceptible epidemic model, we introduce these required conditions explicitly and further prove that they are satisfied by our coarse-grained network construction within the annealed network approximation. Finally, we numerically show that the phase transitions and fluctuations on the coarse-grained network are all in good agreements with those on the original one.

We analyze the granular Rayleigh-Taylor instability of densely packed grains immersed in a compressible or an incompressible fluid using numerical simulations and two types of experiments. The simulations are based on a two-dimensional (2D) molecular dynamics model and the experiments have been carried out in systems of grains immersed in water/glycerol (incompressible fluid) and in air (compressible fluid). The variation of the interstitial fluid is shown to generate different dynamical patterns and mixing properties of the granular systems. The results have been quantified using 2D autocorrelation functions, the power spectrum of the velocity field and velocity field histograms. Excellent agreement is found between the numerical simulations and the experiments.

In this paper we discuss the stability behavior of spherical polyelectrolyte brushes (SPB) in the presence of trivalent lanthanum counterions. Stability behavior is measured through the rate of coagulation of the SPB as a function of the lanthanum concentration using simultaneous static and dynamic light scattering. As the counterion concentration increases, we observe coagulation of the SPB which in turn leads to a dramatic decrease in the stability of our particles. Since the rate of coagulation is dependent upon the balance between the repulsive interactions and the thermal energy of the diffusing particles (reaction-limited colloidal aggregation; RLCA), we then can relate the measured particle stability to the value of the repulsive potential in the RLCA regime. These “microsurface potential measurements” (MSPM) allow us to measure repulsive energies down to the order of $k_{B}T$. From the repulsive energy of the particles we can then determine precise information about the net surface potential ${\Psi }_0$ of the SPB as a function of the lanthanum counterion concentration. Moreover, we demonstrate that a simple mean-field model predicts the stability of the SPB in the presence of lanthanum counterions with high accuracy.

We investigate the phenomenon of selection via flatness. In the static case, the finiteness of the population does not seriously influence the increase of mean fitness of population due to flatness around a peak. The effect is proportional to $1/\sqrt{L}$, where $L$ is the genome length. We investigated the two peak model (high peak and a flat peak). We find that the selection of flatness for long genome lengths occurs as a dynamic phenomenon in the case of evolution with small populations. We found that two factors are crucial to define the role of flatness: special initial distribution (the population is located at centers of peaks) allows flat peak to attract more population, and the large value of mutations per population per virus life cycle sometimes also increases the role of flatness. We suggested simple criteria to identify the phenomenon of dynamical arresting of population around flat peak by experiment. We infer that selection via robustness is possible in evolution as a nonequilibrium phenomenon.

Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency, revealing a “resonant” frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate.

We calculate the mean fitness for evolution models, when the fitness is a function of the Hamming distance from a reference sequence, and there is a probability that this fitness is nullified (Eigen model case) or tends to the negative infinity (Crow-Kimura model case). We calculate the mean fitness of these models. The mean fitness is calculated also for the random fitnesses with logarithmic-normal distribution, reasonably describing sometimes the situation with RNA viruses.

We propose a first-principles model for the dynamic self-assembly of magnetic structures at a water-air interface reported in earlier experiments. The model is based on the Navier-Stokes equation for liquids in shallow water approximation coupled to Newton equations for interacting magnetic particles suspended at a water-air interface. The model reproduces most of the observed phenomenology, including spontaneous formation of magnetic snakelike structures, generation of large-scale vortex flows, complex ferromagnetic-antiferromagnetic ordering of the snake, and self-propulsion of bead-snake hybrids.

Synchronizing nonidentical chaotic oscillators is very often achieved by using various types of couplings. In the practice of synchronization the “right choice” of the coupling variable—$y$ for the Rössler system, $x$ for the Lorenz equations, and so on—is usually stated rather than explained or justified. Using the Rössler and Rucklidge system, in this paper, it is shown that such “optimal” choices are strongly related to observability properties which, in turn, can be quantified. In this paper it will also be shown that synchronizability does not only depend on the observability of the system but it is also a consequence of the dynamical regimes under study. The paper aims at providing important insight into the critical problem of making the “right choice” when it comes to choosing the coupling variable in synchronization schemes.

Turbulent Rayleigh-Bénard convection in a closed cylindrical cell is studied in the Lagrangian frame of reference with the help of three-dimensional direct numerical simulations. The aspect ratio of the cell $\Gamma$ is varied between 1 and 12, and the Rayleigh number Ra between ${10}^7$ and ${10}^9$. The Prandtl number Pr is fixed at 0.7. It is found that both the pair dispersion of the Lagrangian tracer particles and the statistics of the acceleration components measured along the particle trajectories depend on the aspect ratio for a fixed Rayleigh number for the parameter range covered in our studies. This suggests that large-scale circulations present in the convection cell affect the Lagrangian dynamics. Our findings are in qualitative agreement with existing Lagrangian laboratory experiments on turbulent convection.

Considering the higher-order nonlinearities in a material can significantly change its behavior. We suggest the extended nonlinear Schrödinger equation to describe the propagation of ultrashort optical pulses through a dispersive medium with higher-order nonlinearities. Soliton trains are generated through the modulational instability and we point out the influence of the septic nonlinearity in the modulational instability gain. Experimental values are used for the numerical simulations and the input plane wave leads to the development of pulse trains, depending upon the sign of the septic nonlinearity.

The aim of the paper is to understand how the inclusion of more and more time scales into a stochastic stationary Markovian process affects its conditional probability. To this end, we consider two Gaussian processes: (i) a short-range correlated process with an infinite set of time scales bounded from above and (ii) a power-law correlated process with an infinite and unbounded set of time scales. For these processes we investigate the equal position conditional probability $P\left(x,t\mid x,0\right)$ and the mean first passage time $T_x\left(\Lambda \right)$. The function $P\left(x,t\mid x,0\right)$ can be considered as a proxy of the persistence, i.e., the fact that when a process reaches a position $x$ then it spends some time around that position value. The mean first passage time can be considered as a proxy of how fast is the process in reaching a position at distance $\Lambda$ starting from position $x$. In the first investigation we show that the more time scales the process includes, the larger is the persistence. Specifically, we show that the power-law correlated process shows a slow power-law decay of $P\left(x,t\mid x,0\right)$ to the stationary probability density function. By contrast, the short-range correlated process shows a decay dominated by an exponential cutoff. Moreover, we also show that the existence of an infinite and unbounded set of time scales is a necessary but not sufficient condition for observing a slow power-law decay of $P\left(x,t\mid x,0\right)$. In fact, in the context of stationary Markovian processes such a form of persistence seems to be associated with the existence of an algebraic decay of the autocorrelation function. In the second investigation, we show that for large values of $\Lambda$ the more time scales the process includes, the larger is the mean first passage time, i.e., the slower is the process. On the other hand, for small values of $\Lambda$, the more time scales the process includes, the smaller is the mean first passage time, i.e., when a process statistically spends more time in a given position the likelihood that it reached nearby positions by chance may also be enhanced.